Question

Rectangle ABCD is similar to rectangle QRST. T т 5 B Given that ABCD has a perimeter of 28 units and QRST has a perimeter of 42 units, what is true about the ratio of the area? (TDE.G.14.a)(1 point) o A. 9:4 B. 4:9 O C. 2:3 D. 8:27

Answer 1

We have the following:

For ABCD:

`\begin{gathered} 28=2\cdot l+2\cdot w=2\cdot6.5+2\cdot7.5=28 \\ a=l\cdot w=6.5\cdot7.5=48.75 \end{gathered}`

42/28 = 1.5

For QRST:

`\begin{gathered} L=1.5\cdot l=1.5\cdot6.5=9.75 \\ W=1.5\cdot w=1.5\cdot7.5=11.25 \\ A=9.75\cdot11.25=109.6875 \end{gathered}`

The rario of the area is:

`(a)/(A)=(48.75)/(109.6875)=(4\cdot12.1875)/(9\cdot12.1875)=(4)/(9)`

Therefore, the rario is B. 4:9